The research proposed here involves developing statistical methodology useful in survival analysis. Problems to be attacked are arranged in six different areas: 1) regression analysis with censored data wherein we propose to examine the general linear model under random censorship, 2) shrinkage estimation methodology to improve nonparametric survival curve estimators, 3) estimation of the survivorship functions when the censoring mechanism is statistically dependent, 4) a Bayesian estimation problem for the bivariate survivorship function under censoring, 5) estimation of the depth density, hazard rate and related classification procedures under censoring and 6) development of computer programs, simulation studies and applications to known data sets for the procedures derived.